Homotopic invariance of dihedral homologies for 𝐴_{∞}-algebras with involution

IF 0.7 4区数学 Q2 MATHEMATICS

St Petersburg Mathematical Journal Pub Date : 2022-10-31 DOI:10.1090/spmj/1736

S. Lapin

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引用次数: 0

Abstract

It is established that the dihedral homologies of involutive A ∞ A_{\infty } -algebras are homotopically invariant with respect to the homotopy equivalences of involutive A ∞ A_{\infty } -algebras. As a consequence, it is shown that over any field, the dihedral homologies of a topological space are isomorphic to the dihedral homologies of the involutive A ∞ A_{\infty } -algebra of homologies for the simplicial group of Kan loops of the original topological space.

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具有对合的𝐴_{∞}-代数的二面体同调不变性

建立了对合A∞A＿的二面体同调{\infty } -代数对于对合A∞A＿的同伦等价是同伦不变的{\infty } -代数。结果表明，在任意域上，拓扑空间的二面体同构与对合a∞A＿的二面体同构是同构的{\infty } 原始拓扑空间的Kan环的简群的-同调代数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

St Petersburg Mathematical Journal MATHEMATICS-

CiteScore

1.00

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.